Finite element approximations of harmonic map heat flows and wave maps into spheres of nonconstant radii

DOI10.1007/s00211-009-0282-yzbMath1203.65174OpenAlexW2040268808MaRDI QIDQ972580

Ľubomír Baňas, Andreas Prohl, Reiner Michael Schätzle

Publication date: 21 May 2010

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-009-0282-y

zbMATH Keywords

Lagrange multipliersnumerical examplesfinite elementharmonic mapheat flowwave map

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) PDEs in connection with fluid mechanics (35Q35) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (4)

Ergodicity for a stochastic geodesic equation in the tangent bundle of the 2D sphere ⋮ Convergence of Renormalized Finite Element Methods for Heat Flow of Harmonic Maps ⋮ MultiSymplectic Discretization of Wave Map Equations ⋮ Fast and accurate finite element approximation of wave maps into spheres

Cites Work

• On the formation of singularities in the critical \(O(3)\) \(\sigma \)-model
• On the evolution of harmonic mappings of Riemannian surfaces
• Existence and partial regularity results for the heat flow for harmonic maps
• Finite-time blow-up of the heat flow of harmonic maps from surfaces
• The weak solutions to the evolution problems of harmonic maps
• Stable discretization of scalar and constrained vectorial Perona-Malik equation
• Renormalization and blow up for charge one equivariant critical wave maps
• Formation of singularities for equivariant (2+1)-dimensional wave maps into the 2-sphere
• Convergent discretization of heat and wave map flows to spheres using approximate discrete Lagrange multipliers
• An Unsymmetric-Pattern Multifrontal Method for Sparse LU Factorization
• Recent Developments in the Modeling, Analysis, and Numerics of Ferromagnetism
• A Convergent and Constraint‐Preserving Finite Element Method for thep‐Harmonic Flow into Spheres
• Constraint preserving implicit finite element discretization of harmonic map flow into spheres
• Finite Element Approximations of Wave Maps into Spheres
• A Convergent Implicit Finite Element Discretization of the Maxwell–Landau–Lifshitz–Gilbert Equation
• Weak solutions and development of singularities of the SU(2) σ‐model
• A New Algorithm For Computing Liquid Crystal Stable Configurations: The Harmonic Mapping Case
• Color image enhancement via chromaticity diffusion
• The wave maps equation
• Dispersion and collapse of wave maps
• Numerical Methods forp-Harmonic Flows and Applications to Image Processing
• CONVERGENCE OF A FINITE ELEMENT DISCRETIZATION FOR THE LANDAU–LIFSHITZ EQUATIONS IN MICROMAGNETISM
• Modeling of Thermally Assisted Magnetodynamics
• Geometric Numerical Integration
• Stability and Convergence of Finite-Element Approximation Schemes for Harmonic Maps
• Convergence of an Implicit Finite Element Method for the Landau–Lifshitz–Gilbert Equation
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